Question: Multiply the following complex numbers: $({-3+5i}) \cdot ({2-5i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-3+5i}) \cdot ({2-5i}) = $ $ ({-3} \cdot {2}) + ({-3} \cdot {-5}i) + ({5}i \cdot {2}) + ({5}i \cdot {-5}i) $ Then simplify the terms: $ (-6) + (15i) + (10i) + (-25 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -6 + (15 + 10)i - 25i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -6 + (15 + 10)i - (-25) $ The result is simplified: $ (-6 + 25) + (25i) = 19+25i $